On dense subspaces in a class of Fréchet function spaces on R^n

Details On dense subspaces in a class of Fréchet function spaces on R^n On dense subspaces in a class of Fréchet function spaces on R^n

1994-12-13

arxiv.org/abs/funct-an/9412003v1

Mathematics

Functional Analysis

14 pages, no figures, plain Tex

Scientific paper

When dealing with concrete problems in a function space on R^n, it is sometimes helpful to have a dense subspace consisting of functions of a particular type, adapted to the problem under consideration. We give a theorem that allows one to write down many of such subspaces in commonly occurring Fr\'echet function spaces. These subspaces are all of the form $\{pf_0 | p\in{\cal P}\}$ where $f_0$ is a fixed function and ${\cal P}$ is an algebra of functions. Classical results like the Stone-Weierstrass theorem for polynomials and the completeness of the Hermite functions are related by this theorem.

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